There is proposed a hard multilayer coated tool that is constituted by (i) a tool substrate made of high-speed tool steel or cemented carbide and (ii) a hard multilayer coating disposed on a surface of the tool substrate. The hard multiplayer coating includes a TiAlN layer and a mixture layer of TiAlN+CrN that are alternately superposed on each other. As an example of the hard multilayer coated tool, Patent Document 1 discloses a rotary cutting tool including a TiAlN layer and a mixture layer that are alternately superposed on each other, wherein the TiAlN layer has a high hardness while the mixture layer includes CrN whose hardness is relatively low. In the disclosed rotary cutting tool, an excellent wear resistance is obtained owing to presence of the TiAlN layer having the high hardness, while an increased tenacity is obtained owing to presence of the mixture layer including CrN whose hardness is relatively low, so that chipping and peeling of the coating is restrained whereby durability of the tool is substantially increased.    Patent Document 1: JP-2002-275618A